Question

The impulse response of an ideal band pass filter is given by the equation: n 0 h(n)=-sin(nw.) wl sin(nw!) nヂ0 Using the above equation, write a Matlab program that implements an approximation for the band pass filter with cut-off frequencies ω1-0.2π rad/sample and c02-0.3t rad/sample. Set the order of the filter to 100 or 101. Use a Bartlett window here. Plot the frequency and phase responses of this digital filter.

Answer 1

MATLAB code is given below in bold letters.

clc;
close all;
clear all;

% define w1 ans w2 as follows
w1 = 0.2*pi;
w2 = 0.3*pi;

% define n as follows
n = -50:50;
h = w2/pi * sin(n*w2)./(n*w2) - w1/pi * sin(n*w1)./(n*w1);
h(51) = w2/pi-w1/pi;

% bartlett window
W = bartlett(length(n))' ;

% modify the filter with bartlett window
h = h .* W;

% plot the impulse response in time domain
figure;stem(n,h);grid on;xlabel('n');title('filter impulse response');
% plot the frequency respons of the filter.
figure;
freqz(h,1);title('frequecny response of the filter');
grid on;

filter impulse response 0.1 0.08 0.06 0.04 0.02 0 0.02 0.04 0.06 0.08 -0.1 -50 40 30 -20 10 0 10 20 30 40 50

fre quecny response of the filter 920 o -40 -60 0 0.1 0.2 0.3 0. 0.5 0.6 0.7 0.80.1 Normalized Frequency (xT rad/sample) -5000 -10000 0 0.1 0.2 0.3 0.4 0.5 0.60.7 0.8 0.91 Normalized Frequency (xT rad/sample)